There is a surge of research devoted to the formalism and physical manifestations of non-Lorentzian kinematical symmetries, which focuses especially on the ones associated with the Galilei and Carroll relativistic limits (the speed of light taken to infinity or to zero, respectively). The investigations have also been extended to quantum deformations of the Carrollian and Galilean symmetries, in the sense of (quantum) Hopf algebras. The case of 2+1 dimensions is particularly worth to study due to both the mathematical nature of the corresponding (classical) theory of gravity, and the recently finalized classification of all quantum-deformed algebras of spacetime isometries. Consequently, the list of all quantum deformations of (anti-)de Sitter-Carroll algebra is immediately provided by its well-known isomorphism with either Poincaré or Euclidean algebra. Quantum contractions from the (anti-)de Sitter to (anti-)de Sitter-Carroll classification allow to almost completely recover the latter. One may therefore conjecture that the analogous contractions from the (anti-)de Sitter to (anti-)de Sitter-Galilei $r$-matrices provide (almost) all coboundary deformations of (anti-)de Sitter-Galilei algebra. This scheme is complemented by deriving (Carrollian and Galilean) quantum contractions of deformations of Poincaré algebra, leading to coboundary deformations of Carroll and Galilei algebras.
Maxwell Institute and School of Mathematics, The University of Edinburgh（爱丁堡大学数学学院）；International School for Advanced Studies (SISSA)（国际高等研究院）；Istituto Nazionale di Fisica Nucleare, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián, sede Valdivia（圣塞巴斯蒂安大学工程学院（瓦尔迪维亚校区））；Erwin Schrödinger Int. Institute for Mathematics and Physics, University of Vienna（维也纳大学埃尔温·薛定谔数学与物理国际研究所）；University of Vienna, Faculty of Physics, Mathematical Physics（维也纳大学物理学院数学物理系）
From Galilei to Euclidean Carroll and the Alice Particle: The Times They Are a-Changin'
Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）；Departamento de Electromagnetismo y Electrónica, Universidad de Murcia（穆尔西亚大学电磁学与电子系）；Division of Theoretical Physics, Rudjer Bošković Institute（鲁德·博什科维奇研究所理论物理部）；Department of Physics, Faculty of Science, University of Zagreb（萨格勒布大学理学院物理系）
探讨广义伽利略极限中光速 c 的变化，通过允许世界体积为欧几里得，使 p 膜伽利略极限变为卡罗尔极限，统一了伽利略和卡罗尔极限方法，还研究了其后果及相关代数和粒子行动。
Carroll Geometry Meets De Sitter Space via Holography
Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Center of Gravity, The Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所引力中心）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）；Universidad Católica de la Santísima Concepción（圣心天主教大学）；Grupo de Investigación en Física Teórica, GIFT, Universidad Católica de la Santísima Concepción（圣心天主教大学理论物理研究组，GIFT）；Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastián（圣塞巴斯蒂安大学工程、建筑与设计学院）；Division of Theoretical Physics, Rudjer Bošković Institute（鲁德·博什科维奇研究所理论物理部）
Carrollian and Galilean conformal higher-spin algebras in any dimensions
我们提出了包含庞加莱子代数的高自旋代数，并与任何时空维度$D \geq 3$中与瓦西里耶夫方程相关的李代数具有相同的生成元集。考虑到这些性质，它们可以被认为是闵可夫斯基空间中高自旋规范理论的候选刚性对称，或者是少一维空间中的卡洛共形高自旋对称。我们建立这些李代数作为$iso(1,D-1)$的通用包络代数的子代数，并展示如何将它们恢复为Anti de Sitter空间中高自旋规范理论的刚性对称的Inönü-Wigner压缩，或者等价地恢复为相对论共形高自旋对称的Inönü-Wigner压缩。我们使用相同的技术，也定义高自旋代数相同的一套发电机和包含伽利略共形子代数，被解释为非相对论限制的共形对称的自由标量场。首先，我们证明了已知的三维平坦空间高自旋代数可以作为$iso(1,2)$的泛包络代数的子代数得到，然后我们沿着同样的路线将分析扩展到一般的时空维数。我们还讨论了$D=5$出现的特点。
Krylov Complexity: Flat bands and Carroll breaking deformations
Birla Institute of Technology and Science, Pilani Campus（比拉理工学院皮拉尼校区）；Department of Physics, Indian Institute of Technology Gandhinagar（印度理工学院艾哈迈达巴德分校物理系）；Department of Physics, Birla Institute of Technology and Science Pilani, Zuarinagar, Goa（比拉理工学院扎伊纳加尔果阿校区物理系）
